Network Methods for Electromagnetic Field. Multiphysics Modeling

Transcription

1 Network Methods for Electromagnetic Field and Multiphysics Modeling Peter Russer and Johannes Russer Institute for Nanoelectronics Technical University Munich, Germany #1

2 Introduction In this presentation we will recall the importance of network techniques for electromagnetic problem formulation and solution. Network methods are applied to the field problem using the segmentation technique and by specifying lumped element equivalent circuits modeling the substructures. Network-oriented methods can add significantly to the problem formulation and solution methodology and to system identification with relative generation of equivalent circuits. #2

3 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Multiphysics Modeling 12. Conclusion #3

4 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Multiphysics Modeling 12. Conclusion #4

5 Circuit Models of Electromagnetic Structures Whereas the electromagnetic field concept provides the fundamental and complete description of electromagnetic phenomea, network models relate integral quantities like voltage and current. The network description represents a higher model hierarchical level than the field description and yields a considerable model simplification in all cases where it is applicable. #5

6 Comparison of Field and Network Concepts #6

7 Segmentation of an Electromagnetic Structure #7

8 Field expansion into Basis Functions Expanding the tangential fields on R l into a complete set of biorthonormal vector basis functions: The expansion coefficients V n l and I n l can be considered as generalized voltages and currents. #8

9 Impedance and Admittance Functions Relating Generalized Voltages and Currents If only electric walls are involved, the admittance representation of the Green s function will be appropriate. If only magnetic walls are involved, the impedance representation will be appropriate. #9

10 The Connection Network Field Theoretic Formulation of Tellegen s Theorem: Topological relationships for fields state the continuity of the transverse component of the electromagnetic field and pose interesting constraints on the choice of independent and dependent fields with consequences for the connection network which represent the discretized form of the topological relationships. #10

11 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Model Order Reduction 12. Conclusion #11

12 Field Theoretic Formulation of Tellegen s Theorem Field Theoretic Formulation of Tellegen s Theorem P. Russer, M. Mongiardo, L.B. Felsen, Electromagnetic field representations and computations in complex structures III: Network representations of the Connection and Subdomain Circuits, International Journal of, Numerical Modelling, Electronic Networks, Devices and Fields, 2002, vol. 15, pp # #12

13 Field Theoretic Formulation of Tellegen s Theorem Expanding the electric and magnetic fields on both sides α and β into basis functions: Network form of Tellegen s theorem: #13

14 Field Theoretic Formulation of Tellegen s Theorem #14

15 Field Theoretic Formulation of Tellegen s Theorem #15

16 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Multiphysics Modeling 12. Conclusion #16

17 The Characterisation of Circuits and Subcircuits Network methods may be applied to electromagnetic Structures partitioned into segments. The electromagnetic field is expanded into basis functions. The expansion coefficients yield the generalized voltages and currents. The segments of the electromagnetic structure define the circuit elements of the corresponding network. The two-dimensional manifold of boundary surfaces separating the subregions define the connection circuit. #17

18 Relation of Electric and Magnetic Fields on the Boundary Surfaces If a region is filled by source-free linear media, the relation between the tangential electric field and the tangential magnetic field on the boundary surface R l may be expressed by either of the integral equations #18

19 The Green s Function Representation #19

20 The Canonical Foster Representation of Distributed Circuits For a linear reciprocal lossless multiportport an equivalent circuit model may be specified by the canonical Foster representation (Cauer1940, Belevitch1968) #20

21 The Canonical Foster Admittance Representation of Distributed Circuits #21

22 The Canonical Foster Admittance Representation of Distributed Circuits #22

23 The Canonical Foster Impedance Representation of Distributed Circuits #23

24 The Canonical Foster Impedance Representation of Distributed Circuits #24

25 The Extended Foster Admittance Representation for Lossy Distributed Circuits T. Mangold, P. Russer, Full-wave modeling and automatic equivalentcircuit generation of millimeter-wave planar and multilayer structures, IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 6, June 1999, pp #25

26 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Multiphysics Modeling 12. Conclusion #26

27 The Cauer Canonic Realization of Radiation Modes The complete electromagnetic structure is embedded in a virtual sphere. Outside the sphere free space is assumed. The field outside the sphere may be expanded into TM and TE spherical waves. P. Russer, Network-oriented modeling of radiating electromagnetic structures, Elektrik Turk. J. Elec. Engin., vol. 10, no. 2, 2002, pp #27

28 The Cauer Canonic Realization of Radiation Modes #28

29 The Cauer Canonic Realization of Radiation Modes #29

30 The Cauer Canonic Realization of Radiation Modes #30

31 The Complete Radiating Electromagnetic Structure In order to establish the equivalent circuit of a reciprocal linear lossless radiating electromagnetic structure, we embed the structure in a sphere. The internal sources 1 and 2 are enclosed in regions R 3 and R 4. Region R 2 contains the reciprocal passive electromagnetic structure. Region R 1 is the the infinite free space region outside the sphere S. #31

32 The Complete Radiating Electromagnetic Structure #32

33 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Multiphysics Modeling 12. Conclusion #33

34 Richards Transformation: Discrete-Time State Equation Approach #34

35 The Transmission Line Segment Circuit (TLSC) Scheme #35

36 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Model Order Reduction 12. Conclusion #36

37 The TLM Cell The continuous space is subdivided into cells. In each surface the tangential electric and magnetic field components are sampled. The wave amplitudes a i and b i are normal to these tangential planes. In the network model of TLM, in each sampling point one port is assigned to each polarization. #37

38 Time Propagation and Scattering #38

39 The TLM Scheme k+1 b > = S k a ># k a > = Γ k b ># M. Krumpholz, P. Russer, A field theoretical derivation of TLM, IEEE Transactions on Microwave Theory and Techniques, Vol. 42, No. 9, September 1994, pp P. Russer, The transmission line matrix method, in Applied Computational Electromagnetics, NATO ASI Series F: Computer and Systems Sciences, vol. F-171, Ed.: N.K. Uzunoglu et al, Springer, Berlin, 2000, pp #39

40 Interdigital Coupling Capacitor (IDCC) Multichip Module (MCM) thinfilm technology materials: - MCM substrate: Al 2 O 3 (ε r =9.8) - dielectric filling: polyamide (ε r =3.3) - copper metallisation (σ ) geometry: - microstrip conductor width ω=60 µm - MCM metalisation thickness: t=5 µm - polyamide thickness h= 25 µm - finger / slot width 10 µm - finger length l f = 450 µm port impedance : 50 Ω #40

41 IDCC:Equivalent Lumped Element Circuit Time domain scattering signals: Laplace transform of scattering signals in admittance representation: Plot of Y21(p), Im{p}=0, Contour plot of Y21(p) Lumped element equivalent circuit: #41

42 IDCC: Comparison TLM Simulation and Computation from Equivalent Circuit Admittance parameters (log.)# Scattering parameters (log.) #42

43 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Model Order Reduction 12. Conclusion #43

44 Model-based Spectral Analysis and System Identification Methods In numerical time-domain simulation of electromagnetic fields the computational effort may be considerably reduced by model-based parameter estimation approaches. System Identification (SI) approaches, which analyze exciting impulses and corresponding transient responses simultaneously, or Spectral Analysis (SA) methods can be used to extract transfer admittance and impedance matrices of electromagnetic systems for the subsequent calculation of their corresponding Foster matrix representations. By this way also compact lumped element equivalent circuits for the distributed circuits may be generated. #44

45 Model-based Spectral Analysis and System Identification Methods P. Russer, A.C. Cangellaris, Network-Oriented Modeling, Complexity Reduction and System Identification Techniques for Electromagnetic Systems, Fourth International Workshop on Computational Electromagnetics in the Time-Domain-TLM FDTD and Related Techniques (CEM-TD), Nottingham, UK, pp , September #45

46 System Identification for Band-Limited Input Signals SI approaches simultaneously determine the model parameters of microwave structures from multivariable input and output data. The Output Error Model for example determines the model parameters through the least square minimization of #46

47 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Multiphysics Modeling 12. Conclusion #47

48 Hybrid TLM Multipole Expansion Method We embed the TLM simulation region in a sphere. Inside the spherical domain the TLM simulation is performed. On the surface of the sphere the TLM boundary cells are matched to spherical waves radiating into the outer region. P. Lorenz, P. Russer, Hybrid transmission line matrix (TLM) and multipole expansion method for timedomain modeling of radiating structures, 2004 Int. Microwave Symp. Digest, Fort Worth. #48

49 Bowtie Antenna A bowtie antenna of dimensions 0.2 x 0.2 m with the flare angle of 90 in free space is considered# The input impedance of the antenna is to be computed# On the figure we see the field distribution below the bowtie patch at one time instance# The input impedance is obtained from one simulation run# #P. Lorenz and P. Russer, Hybrid Transmission Line Matrix-Multipole Expansion (TLMME) Method, International Conference on Electromagnetics in Advanced Applications (ICEAA 05), Torino, Sept , 2005.# #49

50 Bowtie Antenna #50

51 Contents 1. Introduction 2. Circuit Models of Electromagnetic Structures 3. Tellegen's Theorem and the Connection Network 4. Foster Representation of Reactance Multiports 5. The Characterisation of Radiation Modes 6. The Discrete Time State Equation Approach 7. The Transmission Line Matrix (TLM) Method 8. Wave Digital Filter Methods 9. Spectral Analysis and System Identification Methods 10. Hybrid Methods 11. Multiphysics Modeling 12. Conclusion #51

52 The Modeling Work flow Electromagnetic Structure Segmentation Space - and Time Discretization TLM - Scheme Model Order Reduction System Identification Modal Expansion Lumped Element Equivalent Circuits (Foster and Cauer Equivalent Circuits) TLSC Models Compact WDF Model #52

53 Multiphysics Modeling The growing importance of nanostructured electronic devices and systems constitute the demand for advanced accurate and efficient multiphysics modeling tools for design and optimization. Multi-physics modeling of complex nanoelectronic structures and devices based on materials and structures like metallic nanoparticles, nanostructured patterned metallic surfaces, carbon nanotubes (CNTs), graphene layers, polymers, semiconductors and superconductors. Modeling of interacting physical phenomena under consideration of large variations of space- and time scales, the time variations of geometry and material parameters Demand for compact model generation and design optimization. #53

54 Multiscale Modeling Subgridding Variable Mesh Subgridding Within short distances the field variations are determined by the electrostatic and magnetostatic field solutions. The computational effort is reduced by static sub-gridding. Magnetostatic field solutions are used to compute correction factors for the larger TLM cells. #54

55 Multiscale Modeling Subgridding Microstrip-stub on a Silicon on Insulator wafer a: measurement b: TLM with fine grid c: TLM with coarse grid d: TLM with static sub-grid W. Dressel and P. Russer, TLM Modelling of Electromagnetic Structures Using Static SubGriddings, 2nd Microwave and Radar Week in Krakow, Poland, MIKON2006, May 22-24, 2006 Vol. 2, pages #55

56 Multiphysics Modeling Lagrange Mapping Applied to Modeling of Electromagnetic Wave Propagation in Media with Moving Deformation v=1*10 7 m/s a=4cm d=1cm Grid spacing: 2.5mm J. A. Russer and A. C. Cangellaris, An efficient methodology for the modelingof electromagnetic wave phenomena in domains with moving boundaries, in IEEE MTT-S International Microwave Symposium, Atlanta, GA, June2008, pp [Online]. Available: #56

57 Workflow for Multiphysics Modeling Physical Structure General Dynamical Description: Langevin / Hamilton Equations Electromagnetic Maxwell s Equations Electron Transport Boltzmann Equations Mechanical Quantum Mechanical Schroedinger Equation Thermal Heat Conduction Global Model, Coupled Equations, Segmentation, Multi-Time Scales Space - and Time Discretization TLM - Scheme Modal Expansion Integral Equation Greens Function Spectral Representation Lumped ElementEquivalent Circuits (Foster and CauerEquivalent Circuits) TLSC Models WDF Models Model Order Reduction System Identification Compact Model #57

58 Conclusion Network-oriented methods contribute significantly to the problem formulation and solution methodology of EM field problems. The field problem may be systematically treated by the segmentation technique. The TLM method as a network model of the electromagnetic field yields a state equation representation of the discretized electromagnetic field. The TLSC method provides a generalization of the TLM method allowing to include also analytic models in time-discrete schemes. The segmentation technique allows hybridization and combination of various analytic and numerical methods. TLSC schemes are directly related to WDF methods. Based upon SI and SA model-based methods lumped element models can be extracted. Network methods are interesting for multi-physics modeling of complex nanoelectronic structures and devices. #58